diff --git a/app/assets/javascripts/label_manager.js b/app/assets/javascripts/label_manager.js
index f134a54dd5361efc4651302324d3e7330881ec89..4d304c5fe69fc5fcab067c0b3d2b72c09ebe5c0b 100644
--- a/app/assets/javascripts/label_manager.js
+++ b/app/assets/javascripts/label_manager.js
@@ -14,13 +14,16 @@ export default class LabelManager {
     this.errorMessage = 'Unable to update label prioritization at this time';
     this.emptyState = document.querySelector('#js-priority-labels-empty-state');
     this.$badgeItemTemplate = $('#js-badge-item-template');
-    this.sortable = Sortable.create(this.prioritizedLabels.get(0), {
-      filter: '.empty-message',
-      forceFallback: true,
-      fallbackClass: 'is-dragging',
-      dataIdAttr: 'data-id',
-      onUpdate: this.onPrioritySortUpdate.bind(this),
-    });
+
+    if ('sortable' in this.prioritizedLabels.data()) {
+      Sortable.create(this.prioritizedLabels.get(0), {
+        filter: '.empty-message',
+        forceFallback: true,
+        fallbackClass: 'is-dragging',
+        dataIdAttr: 'data-id',
+        onUpdate: this.onPrioritySortUpdate.bind(this),
+      });
+    }
     this.bindEvents();
   }
 
diff --git a/app/assets/stylesheets/pages/labels.scss b/app/assets/stylesheets/pages/labels.scss
index e3d0d0b0fa2e68ad5dc271222e17d67669cd037f..60a840aac1b75a6026446f6205a941a0fb636d6b 100644
--- a/app/assets/stylesheets/pages/labels.scss
+++ b/app/assets/stylesheets/pages/labels.scss
@@ -75,7 +75,7 @@
   padding: 0;
   margin-bottom: 0;
 
-  > li:not(.empty-message):not(.is-not-draggable) {
+  > li:not(.empty-message):not(.no-border) {
     background-color: $white-light;
     margin-bottom: 5px;
     display: flex;
@@ -92,7 +92,7 @@
       opacity: 0.3;
     }
 
-    .prioritized-labels & {
+    .prioritized-labels:not(.is-not-draggable) & {
       box-shadow: 0 1px 2px $issue-boards-card-shadow;
       cursor: move;
       cursor: grab;
@@ -353,7 +353,7 @@
 
 @media (max-width: map-get($grid-breakpoints, md)-1) {
   .manage-labels-list {
-    > li:not(.empty-message):not(.is-not-draggable) {
+    > li:not(.empty-message):not(.no-border) {
       flex-wrap: wrap;
     }
 
diff --git a/app/views/projects/labels/index.html.haml b/app/views/projects/labels/index.html.haml
index bb7c297ba1ffb5e573d34c8df36a48cd5dc509d9..5d73d832170d0c406d1ada39e2987ac27de6b59e 100644
--- a/app/views/projects/labels/index.html.haml
+++ b/app/views/projects/labels/index.html.haml
@@ -11,29 +11,28 @@
     = render 'shared/labels/nav', labels_or_filters: labels_or_filters, can_admin_label: can_admin_label
 
     .labels-container.prepend-top-10
-      - if can_admin_label
-        - if search.blank?
-          %p.text-muted
-            = _('Labels can be applied to issues and merge requests.')
-            %br
-            = _('Star a label to make it a priority label. Order the prioritized labels to change their relative priority, by dragging.')
-        -# Only show it in the first page
-        - hide = @available_labels.empty? || (params[:page].present? && params[:page] != '1')
-        .prioritized-labels{ class: ('hide' if hide) }
-          %h5.prepend-top-10= _('Prioritized Labels')
-          .content-list.manage-labels-list.js-prioritized-labels{ "data-url" => set_priorities_project_labels_path(@project) }
-            #js-priority-labels-empty-state.priority-labels-empty-state{ class: "#{'hidden' unless @prioritized_labels.empty? && search.blank?}" }
-              = render 'shared/empty_states/priority_labels'
-            - if @prioritized_labels.present?
-              = render partial: 'shared/label', subject: @project, collection: @prioritized_labels, as: :label, locals: { force_priority: true }
-            - elsif search.present?
-              .nothing-here-block
-                = _('No prioritised labels with such name or description')
+      - if can_admin_label && search.blank?
+        %p.text-muted
+          = _('Labels can be applied to issues and merge requests.')
+          %br
+          = _('Star a label to make it a priority label. Order the prioritized labels to change their relative priority, by dragging.')
+
+      -# Only show it in the first page
+      - hide = @available_labels.empty? || (params[:page].present? && params[:page] != '1')
+      .prioritized-labels{ class: [('hide' if hide), ('is-not-draggable' unless can_admin_label)] }
+        %h5.prepend-top-10= _('Prioritized Labels')
+        .content-list.manage-labels-list.js-prioritized-labels{ data: { url: set_priorities_project_labels_path(@project), sortable: can_admin_label } }
+          #js-priority-labels-empty-state.priority-labels-empty-state{ class: "#{'hidden' unless @prioritized_labels.empty? && search.blank?}" }
+            = render 'shared/empty_states/priority_labels'
+          - if @prioritized_labels.present?
+            = render partial: 'shared/label', subject: @project, collection: @prioritized_labels, as: :label, locals: { force_priority: true }
+          - elsif search.present?
+            .nothing-here-block
+              = _('No prioritised labels with such name or description')
 
       - if @labels.present?
         .other-labels
-          - if can_admin_label
-            %h5{ class: ('hide' if hide) }= _('Other Labels')
+          %h5{ class: ('hide' if hide) }= _('Other Labels')
           .content-list.manage-labels-list.js-other-labels
             = render partial: 'shared/label', subject: @project, collection: @labels, as: :label
             = paginate @labels, theme: 'gitlab'
diff --git a/app/views/shared/milestones/_labels_tab.html.haml b/app/views/shared/milestones/_labels_tab.html.haml
index 6b0640bd8cbc6b227b45e4554af8dea92da4d2c4..ecab037e378d8c59711e5e6321ded62aed9f36ce 100644
--- a/app/views/shared/milestones/_labels_tab.html.haml
+++ b/app/views/shared/milestones/_labels_tab.html.haml
@@ -2,7 +2,7 @@
   - labels.each do |label|
     - options = { milestone_title: @milestone.title, label_name: label.title }
 
-    %li.is-not-draggable
+    %li.no-border
       %span.label-row
         %span.label-name
           = render_label(label, tooltip: false, link: milestones_label_path(options))
diff --git a/changelogs/unreleased/57247-show-prioritized-labels-to-guests.yml b/changelogs/unreleased/57247-show-prioritized-labels-to-guests.yml
new file mode 100644
index 0000000000000000000000000000000000000000..5210ff0ccef640a334b5a66247d2210da4151cd2
--- /dev/null
+++ b/changelogs/unreleased/57247-show-prioritized-labels-to-guests.yml
@@ -0,0 +1,5 @@
+---
+title: Show prioritized labels to guests
+merge_request: 27307
+author:
+type: fixed
diff --git a/spec/features/projects/labels/update_prioritization_spec.rb b/spec/features/projects/labels/update_prioritization_spec.rb
index d36f043f8800eac8e0ecbb0ec468234c8bc5a5dd..f32b155790fcea0a8b4562bd47021795cedd253d 100644
--- a/spec/features/projects/labels/update_prioritization_spec.rb
+++ b/spec/features/projects/labels/update_prioritization_spec.rb
@@ -138,29 +138,41 @@ describe 'Prioritize labels' do
   end
 
   context 'as a guest' do
-    it 'does not prioritize labels' do
+    before do
+      create(:label_priority, project: project, label: bug, priority: 1)
+      create(:label_priority, project: project, label: feature, priority: 2)
+
       guest = create(:user)
 
       sign_in guest
 
       visit project_labels_path(project)
+    end
 
+    it 'cannot prioritize labels' do
       expect(page).to have_content 'bug'
       expect(page).to have_content 'wontfix'
       expect(page).to have_content 'feature'
-      expect(page).not_to have_css('.prioritized-labels')
       expect(page).not_to have_content 'Star a label'
     end
+
+    it 'cannot sort prioritized labels', :js do
+      drag_to(selector: '.prioritized-labels .label-list-item', from_index: 1, to_index: 2)
+
+      page.within('.prioritized-labels') do
+        expect(first('.label-list-item')).to have_content('bug')
+        expect(page.all('.label-list-item').last).to have_content('feature')
+      end
+    end
   end
 
   context 'as a non signed in user' do
-    it 'does not prioritize labels' do
+    it 'cannot prioritize labels' do
       visit project_labels_path(project)
 
       expect(page).to have_content 'bug'
       expect(page).to have_content 'wontfix'
       expect(page).to have_content 'feature'
-      expect(page).not_to have_css('.prioritized-labels')
       expect(page).not_to have_content 'Star a label'
     end
   end
diff --git a/spec/features/projects/labels/user_views_labels_spec.rb b/spec/features/projects/labels/user_views_labels_spec.rb
index 2c8267764bd0470bdaa0ce43b1ce9f87b854f217..a6f7968c535f89f59dbf29cfe5626ed441afa694 100644
--- a/spec/features/projects/labels/user_views_labels_spec.rb
+++ b/spec/features/projects/labels/user_views_labels_spec.rb
@@ -7,6 +7,7 @@ describe "User views labels" do
   set(:user) { create(:user) }
 
   let(:label_titles) { %w[bug enhancement feature] }
+  let!(:prioritized_label) { create(:label, project: project, title: 'prioritized-label-name', priority: 1) }
 
   before do
     label_titles.each { |title| create(:label, project: project, title: title) }
@@ -18,6 +19,10 @@ describe "User views labels" do
   end
 
   it "shows all labels" do
+    page.within('.prioritized-labels .manage-labels-list') do
+      expect(page).to have_content('prioritized-label-name')
+    end
+
     page.within('.other-labels .manage-labels-list') do
       label_titles.each { |title| expect(page).to have_content(title) }
     end